Contact your luggage manufacturer or bag-maker to ask about the replacement parts they offer for your piece of luggage. While you're at it, ask if there are replacement services for your bag available under your warranty. It always helps to know the facts before your time of need.
Search for your repair parts at a repair store or website if your manufacturer is unable to help you. Sites like OhioTravelBag.com and eBay Luggage carry parts from a variety of manufacturers.
Examine the damage to determine whether or not you can repair the item yourself. Telescoping handles are easily repaired by unscrewing the handle from your suitcase from the inside of the bag, and then screwing the new handle in its place. If you own a sewing machine, it's easy to re-attach cloth handles or straps, too. Use a hair dryer's high heat to smooth out dents in the suitcase exterior.
Find a local luggage repair shop for repairs on wheels or zippers. You may want to carry the manufacturer's replacement parts with you on trips, in case your luggage fails while you're on vacation.